Successive stages of magnetic ordering in the process of magnetisation switching have been studied by means of micromagnetic computations in planar elliptical nanoparticles of hexagonal Cobalt. An external magnetic field was aligned along the easy direction implied by the shape anisotropy, i.e. parallel to the ellipse's major axis, whereas the magnetocrystalline easy axis coincided with the ellipse's minor axis. With increasing size of the particles three different types of magnetisation reversal scenarios have been identified: i) quasi coherent rotation, smooth or flipping-like, of a single domain with all spins staying in the plane of the ellipse, ii) a switch-over with intermediate states characterised by different number of in-plane domains separated by Néel type domain walls (DWs), and iii) occurrence of sharp out-of-plane spikes of magnetisation in the regions of DW, which take on characteristics of vortex domain boundaries. The nature of DWs changes in the latter case from the Néel type, throughout most of their area, to the Bloch type in the vicinity of the spikes. The passages between different domain arrangements within scenarios ii) and iii) show characteristics typical of phase transitions. In particular, analogues of order parameters undergo discontinuous or quasi-continuous variations with the corresponding wider or narrower magnetic hysteresis. Critical exponents are identifiable in the quasi-continuous cases in spite of the finite size of the system. These results disclose a multitude of field-dependent critical sizes in the class of the nanoparticles studied.